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The Astrophysical Journal, 895:47 (10pp), 2020 May 20 https://doi.org/10.3847/1538-4357/ab88a3 © 2020. The American Astronomical Society. All rights reserved.

Tuning the Exospace Radio for Stellar Coronal Mass Ejections

Julián D. Alvarado-Gómez1,2,8 , Jeremy J. Drake2 , Federico Fraschetti2,3 , Cecilia Garraffo2,4 , Ofer Cohen5 , Christian Vocks1 , Katja Poppenhäger1 ,Sofia P. Moschou2 , Rakesh K. Yadav6 , and Ward B. Manchester IV7 1 Leibniz Institute for Astrophysics Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany; [email protected] 2 Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 3 Dept. of Planetary Sciences-Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ, 85721, USA 4 Institute for Applied Computational Science, Harvard University, Cambridge, MA 02138, USA 5 University of Massachusetts at Lowell, Department of Physics & Applied Physics, 600 Suffolk Street, Lowell, MA 01854, USA 6 Department of and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA 7 Department of Climate and Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109, USA Received 2020 March 5; revised 2020 April 9; accepted 2020 April 10; published 2020 May 22

Abstract Coronal mass ejections (CMEs) on other than the have proven very difficult to detect. One promising pathway lies in the detection of typeII radio bursts. Their appearance and distinctive properties are associated with the development of an outward propagating CME-driven shock. However, dedicated radio searches have not been able to identify these transient features in other stars. Large Alfvén speeds and the magnetic suppression of CMEs in active stars have been proposed to render stellar eruptions “radio-quiet.” Employing 3D magnetohydrodynamic simulations, we study the distribution of the coronal Alfvén speed, focusing on two cases representative of a young Sun-like and a mid-activity M-dwarf (). These results are compared with a standard solar simulation and used to characterize the shock-prone regions in the and . Furthermore, using a flux-rope eruption model, we drive realistic CME events within our M-dwarf simulation. We consider eruptions with different energies to probe the regimes of weak and partial CME magnetic confinement. While these CMEs are able to generate shocks in the corona, those are pushed much farther out compared to their solar counterparts. This drastically reduces the resulting type II radio burst frequencies down to the ionospheric cutoff, which impedes their detection with ground-based instrumentation. Unified Thesaurus concepts: Magnetohydrodynamical simulations (1966); Solar flares (1496); Stellar flares (1603); Solar coronal mass ejections (310); Solar shocks (1997); Stellar (1636); (1534); (1522); Stellar magnetic fields (1610); Solar magnetic fields (1503); Stellar coronae (305); Radio bursts (1339)

1. Introduction populations (e.g., Davenport 2016; Guarcello et al. 2019; Ilin et al. 2019). This wealth of information is increasingly driving Flares and coronal mass ejections (CMEs) are more energetic the study of their effects on atmospheres (e.g., than any other class of . These events involve ) ( ) 33 Segura et al. 2010; Mullan & Bais 2018; Tilley et al. 2019 . the rapid seconds to hours release of up to 10 erg of On the other hand, the observational evidence for stellar CMEs magnetic energy in the form of particle acceleration, heating, ( is very thin, with a single direct detection of an extreme event radiation, and bulk motion Webb & Howard 2012; recently reported by Argiroffi et al. (2019) using Chandra. ) ( Benz 2017 . Displaying much larger energies by several Unfortunately, current X-ray instrumentation renders the metho- ) orders of , their stellar counterparts are expected to dology of this detection—resolving (temporally and spectro- play a fundamental role in shaping the evolution of activity and scopically) apost-flare blueshift signature in cool coronal lines— rotation (Drake et al. 2013; Cranmer 2017; Odert et al. 2017), sensitive only to the most energetic eruptions. As described by as well as the environmental conditions around low-mass stars Moschou et al. (2019), other diagnostics, such as asymmetries in (see e.g., Micela 2018). Energetic photon and particle radiation Balmer lines or continued X-ray absorption during flares, have associated with flares and CMEs are also the dominant factors provided only a handful of good CME candidates so far (see also driving the evaporation, erosion, and chemistry of protoplane- Moschou et al. 2017;Vidaetal.2019). tary disks (e.g., Glassgold et al. 1997; Turner & Drake 2009; Analogous to the Sun, an alternative way of recognizing Fraschetti et al. 2018) and planetary atmospheres (e.g., CMEs in distant stars lies in the detection of the so-called type Lammer 2013; Cerenkov et al. 2017; Tilley et al. 2019). This II radio bursts (Wild & McCready 1950; Kundu 1965; Osten & is critical for in the close-in habitable zones around Wolk 2017). These transients correspond to two distinct bright M-dwarfs, which are the focus of recent efforts to locate nearby lanes in radio spectra in the kHz–MHz range, separated by a habitable (Nutzman & Charbonneau 2008; Tuomi et al. factor of ∼2 in frequency, characterized by a gradual drift from 2019), but are known for their long sustained periods of high high to low frequencies. These features are attributed to flare activity (see Osten 2016; Davenport et al. 2019). emission at the fundamental and first harmonic of the plasma 9 Stellar flares are now routinely detected across all wave- frequency, resulting from non-thermal accelerated by lengths from radio to X-ray, spectral types from F-type to brown dwarfs, and ages from stellar birth to old disk 9 -12 Expressed in c.g.s. units as npp = ()(24 peme ) n, where e, m are the charge and mass, and n denotes the number density of the ambient 8 Karl Schwarzschild Fellow. region.

1 The Astrophysical Journal, 895:47 (10pp), 2020 May 20 Alvarado-Gómez et al. a shock generated as the velocity of the CME in the Furthermore, we test the hypothesis of radio-quiet CMEs in frame surpasses the local Alfvén speed (i.e., U CME- V SW > M-dwarfs by simulating eruptions in the regimes of weak and SW fi fi VA = B 4pr , with V , B and ρ as the stellar wind speed, partial large-scale magnetic eld con nement, and determine magnetic field strength and plasma density, respectively10). The whether or not they become super-Alfvénic during their frequency drift reflects the decrease in particle density with temporal evolution. distance as the CME shock propagates outward in the corona This paper is organized as follows: Section 2 contains a (see Cairns et al. 2003; Pick et al. 2006 and references therein). description of the employed models and boundary conditions. While solar observations indicate an association rate of just Results from the steady-state Alfvén speed distributions, as ∼1%–4% between CMEs and type II bursts in general (see well as the time-dependent M-dwarf CME simulations, are Gopalswamy et al. 2005; Bilenko 2018), it is close to 100% for presented in Section 3. We discuss our findings and their the most energetic eruptions (Gopalswamy et al. 2009, 2019). implications in Section 4, and provide a brief summary in Furthermore, the high fraction of CMEs associated with strong Section 5. flares in the Sun (∼80%–90% for X-class flares, see Yashiro & Gopalswamy 2009; Compagnino et al. 2017), combined with 2. Models fl ( the enhanced stellar are rates and energies e.g., Kashyap et al. The numerical simulations discussed in this work follow 2002; Caramazza et al. 2007; Shibayama et al. 2013; Loyd closely the methodology described in Alvarado-Gómez et al. ) et al. 2018 , are expected to yield enough type II burst events in (2018, 2019b), where different models included in the Space active stars to secure detections. While several other radio Weather Modeling Framework11 (SWMF, Gombosi et al. transients have been detected in low-mass stars (see e.g., 2018) were used. Villadsen & Hallinan 2019), this particular class of radio event has not been observed so far (e.g., Crosley et al. 2016; 2.1. Steady-state Configurations Villadsen 2017; Crosley & Osten 2018a, 2018b). However, based on solar statistics it is clear that the lack of typeII bursts The corona and stellar wind solutions are based on the 3D ( ) does not imply an absence of CMEs. MHD code BATS-R-US Powell et al. 1999; Tóth et al. 2012 and the data-driven Alfvén Wave Solar Model (AWSoM, van Recent numerical studies have started to provide a common ) framework to interpret these observations and the apparent der Holst et al. 2014 . The latter, extensively validated and fl updated against remote and solar data (e.g., Oran et al. imbalance between are and CME occurrence in stars. Detailed ) MHD models have shown that the stellar large-scale magnetic 2017; Sachdeva et al. 2019; van der Holst et al. 2019 , field can establish a suppression threshold preventing CMEs of considers Alfvén wave turbulent dissipation as the main driver of coronal heating and stellar wind acceleration. Both certain energies from escaping (Drake et al. 2016; Alvarado- contributions are self-consistently calculated and incorporated Gómez et al. 2018). The rationale of this mechanism comes as additional source terms in the energy and momentum from solar observations, where it has been proposed to operate equations, which, combined with the mass conservation and on smaller scales, forming a magnetic cage for the plasma magnetic field induction equations, close the non-ideal MHD ejecta in certain flare-rich CME-poor active regions (e.g., Sun ) set of equations solved numerically. Radiative losses and et al. 2015; Thalmann et al. 2015, 2017 , preventing access to effects from electron heat conduction are also taken into open-field sectors that could facilitate breakout (Liu et al. 2016; ∼ ) account. Our simulation domain extends from 1 R★ to 85 R★, DeRosa & Barnes 2018 . and employs a radially stretched spherical grid with a The results of Alvarado-Gómez et al. (2018) predict that due maximum base resolution of 0.025 R★, with the to magnetic suppression, escaping stellar CMEs will be slower axis aligned with the z Cartesian direction. and less energetic compared to similar events occurring under The simulation evolves until a steady-state is reached. For ( ) fi weaker or negligible large-scale elds. In a recent observa- solar models, the distribution of the photospheric magnetic field ( ) tional study performed by Villadsen & Hallinan 2019 , low averaged over one rotation (known as a synoptic ), CME velocities compared with the local Alfvén speed were serves as the inner boundary condition from which the Alfvén  considered a possible explanation for the lack of type II events wave dissipation spectrum is constructed (see van der Holst et al. in very active, radio bursting M-dwarfs. Using 1D models and 2014 for details). Our solar run is based on the synoptic scaling laws, Mullan & Paudel (2019) suggested that CMEs in magnetogram12 associated with Carrington rotation (CR) 2107 M-dwarfs would be radio-quiet, as they would not be able to (2011 February/March, rising phase of cycle 24). We use this overcome the large Alfvén speeds in the corona that are the particular CR because its resulting AWSoM solution has been product of the strong surface magnetic fields present on these well studied in previous numerical works (e.g., Sokolov et al. stars (see Donati 2011; Reiners 2014; Shulyak et al. 2019). 2013; Jin et al. 2017a, 2017b). However, for the purposes of Here, we expand and complement these previous ideas, this study, any CR with the presence of AR groups could serve analyzing the Alfvén speed distributions resulting from realistic to drive the reference model. Apart from the CR magnetogram, 3D state-of-the-art corona and stellar wind models. We solar chromospheric levels of plasma density (n0=2× 10 −3 4 compare results for the Sun during an active period, for a 10 cm ) and (T0=5×10 K) are also set at large-scale dipole-dominated geometry representative of a the simulation inner boundary. Default values are used for the young Sun-like star, and for a high-complexity strong field remaining parameters of AWSoM. This includes the propor- distribution predicted from a dynamo simulation of a fully tionality constants for the Alfvén wave Poynting flux 6 −2 −1 convective M-dwarf (Proxima Centauri, Yadav et al. 2016). (SB)★ =´1.1 10 Wm T , and correlation length

10 / fi 11 In a low-density strong- eld regime, the expression for the Alfvén speed http://csem.engin.umich.edu/tools/swmf/ fi 22 12 should be modi ed as VcA =+14pr cB, where c is the . Acquired by the Global Oscillation Network Group (GONG) https://gong. / / / This prevents VA from being larger thanc. nso.edu data magmap .

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Table 1 Set of Parameters Assumed in the Steady-state Simulations Using AWSoM

Model áBñS M★ R★ Prot n0 T0 ()SB★ L^ B −3 −2 −1 Distribution (G)(Me)(Re)(days)(cm )(K)(Wm T )(m T ) Sun CR 2107 3.0 1.0 1.0 25.38 2×1010 5×104 1.1×106 1.5×105 Sun-like CR 2107 +(75 G)a 42.6 1.0 1.0 25.38 2×1010 5×104 1.1×106 1.5×105 M-dwarf Proxima Centaurib 448.8 0.122 0.155 83.0 2×1010 5×104 1.1×106 6.0×105

Notes. a Added to the first term in the spherical harmonic expansion of the surface magnetic field (large-scale dipole). b Snapshot at 490 rotations from the high-resolution dynamo simulation of Yadav et al. (2016).

5 L^ B =´1.5 10 m T (Table 1 in van der Holst et al. Proxima Centauri, two different methods have been used to 2014; see also Sokolov et al. 2013 for more details). constrain the mass-loss rate associated with its stellar wind. An As mentioned earlier, these boundary conditions have been upper limit of MM< 0.2  was placed by Wood et al. (2001), thoroughly tested in several AWSoM validations. We preserve through the astrospheric signature in the Lyα line (Linsky & all of them in our Sun-like dipole-dominated case, modifying Wood 2014). A higher limit of M < 14 M  was found by only the surface field distribution to include a large-scale 75G Wargelin & Drake (2002), measuring in X-rays the direct dipolar component (as described in Alvarado-Gómez et al. signature of charge exchange between the stellar wind and 2018). For this stellar model (and our reference simulation of the local . the Sun), we assumed fiducial solar values of mass As the astrospheric method has been more commonly 13 5  (MM★ = ), radius (R★ = R), and rotation period (Prot= applied, we set L^ B =´6.0 10 m T which yields a 25.38 days). For the comparative analysis presented here, we stellar wind mass-loss rate of M  0.3 M , which is still do not consider the influence of a shorter rotation period consistent with the Lyα limit (taking into account the typical expected from a younger Sun. Still, as noted in Alvarado- errors of this technique; see Linsky & Wood 2014). This is the Gómez et al. (2018), the resulting AWSoM solution in this case same L^ B value used in the stellar wind simulations of is consistent with observational constraints of stellar winds in Proxima Centauri by Garraffo et al. (2016b), and Barnard’s young late-type stars (see Wood et al. 2005), which display Star by Alvarado-Gómez et al. (2019c). Finally, published comparable field strengths and geometries to the one assumed stellar properties for this object are used in this case ( = here (e.g., ξ Boo A, Morgenthaler et al. 2012; ò Eri, Jeffers M★ = 0.122 Me, R★ = 0.154 Re, Prot 83.0 days, Kiraga et al. 2014, 2017). & Stepien 2007; Collins et al. 2017; Kervella et al. 2017). The boundary conditions for the M-dwarf regime are much Table 1 contains a summary of all the parameters considered in less constrained by observations. Here we employ the same our AWSoM steady-state simulations. driving conditions as in Alvarado-Gómez et al. (2019b), using the field topology emerging at the cyclic regime of a 3D 2.2. Flux-rope CME Model dynamo simulation tailored to Proxima Centauri (Yadav et al. The Titov & Démoulin (TD 1999) flux-rope eruption model 2016). We scale the surface radial field between ±1400G, is used to drive our M-dwarf CME simulations. In the SWMF which yields an average field strength compatible with the implementation (e.g., Manchester et al. 2008; Jin et al. 2013), lower bound from Zeeman broadening measurements on this the twisted loop-like structure of the TD model is coupled to star (600 ± 150 G, Reiners & Basri 2008) of ∼450G. the AWSoM steady-state solution at the inner boundary (stellar The presence of strong and complex surface magnetic fields surface), and initialized with eight different parameters related is expected to drastically influence the coronal structure and to the location (2), orientation, size (3), magnetic free energy ( ( FR) fl ( FR) stellar wind e.g., Vidotto et al. 2014; Garraffo et al. 2016a; EB , and mass of the ux-rope M . The CME simulations Cohen et al. 2017). From the AWSoM perspective, this could discussed here use the same parameters as in Alvarado-Gómez imply that additional modifications (apart from the surface et al. (2019b), namely, longitude (270°), latitude (36°), tilt magnetogram) to the boundary conditions might be required. angle (28°), flux-tube radius (20 Mm), length (∼150 Mm), and However, as discussed by Sokolov et al. (2013), the scaling loaded mass (MFR=4.0× 1014 g). We consider two values fl FR ( FR (SB)★ in the Alfvén wave Poynting ux is consistent and of EB in order to probe the regimes of weak EB,1  fl 35 ) ( FR 35 ) equivalent to the magnetic to X-ray ux empirical relation of 4.1´ 10 erg and partial EB,2  2.0´ 10 erg large-scale Pevtsov et al. (2003), which extends beyond the magnetic magnetic CME confinement.14 Note that assuming a similar fluxes observed in M-dwarfs stars. For this reason, we retain flare-CME magnetic energy partition as in the Sun (e.g., Emslie ) FR the standard AWSoM value for this parameter in our Proxima et al. 2012; Toriumi et al. 2017 , our selected EB values are Centauri simulations. consistent and sufficient to power the best CME candidate 31 On the other hand, we consider the currently available observed in Proxima Centauri so far (FX ; 1.7×10 erg, CME 31 ) information on M-dwarf stellar winds to adjust the normal- EK  510´ erg; see Moschou et al. 2019 . The initial ization for the Alfvén wave correlation length L^ B . Unfortunately, stellar wind properties in low mass stars 13 For completeness, we also performed a simulation using the default (particularly M-dwarfs) are highly uncertain. Estimates of AWSoM value for L^ B . The resulting stellar wind mass-loss rate in this case   mass-loss rates (M )—interpreted as a measure of wind strength is M  0.09 M. 14 —are only available for 14 stellar systems (12 detections, 2 This was necessary because in the Proxima-like ±1400G surface field scaling employed here, the CME event simulated in Alvarado-Gómez et al. upper limits), of which only 3 are M-dwarfs (2 detections, 1 ( ) FR 34 fi 2019b , with EB  6.57´ 10 erg, was fully con ned by the large-scale upper limit; see Wood 2018). For the particular case of magnetic field.

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Table 2 true when evaluated on an equivalent latitude with respect to Flux Rope Parameters Initializing the TD CME Simulations within the the large-scale magnetic field dipolar distribution. M-dwarf Model Finally, it is worth noting that along the (∼0° in the Parameter Value Unit Sun-like case, ∼30° in the M-dwarf model), the Alfvén and stellar wind speeds are relatively small (i.e., V <1000 km s−1, Latitude 36.0 deg A VSW „ 100 km s−1), whereas for other latitudes both quantities Longitude 270.0 deg ( ) Tilt anglea 28.0 deg increase rapidly particularly VA . As mentioned earlier, this will Radius (RFR) 20.0 Mm have important consequences for where in the stellar corona the Length (LFR) 150.0 Mm conditions are more favorable for the escaping CMEs—or only Mass (MFR) 4.0×1014 g certain regions of the expanding structure— to become super ( FR) b × 35 Alfvénic. This also clearly shows the importance of the geometry of Magnetic energy EB 4.1 10 erg fi / c × 35 the large-scale magnetic eld and the need for 3D stellar wind 2.0 10 corona descriptions, neither of which are properly captured in simpler 1D, or even 2D rotationally symmetric models. Notes. a Measured with respect to the stellar in the counterclockwise The importance of the bimodal solar wind for the promotion of direction. CME-driven shock formation has been shown in Manchester et al. b ( ) Weakly confined CME. 2005 . c Partially confined CME. 3.2. CME Evolution: Magnetic Suppression and Alfvénic Regimes parameters assumed in our TD flux-rope simulations are listed in Table 2. We now consider the results from the time-dependent CME Each CME simulation evolves for 90 minutes (real time) simulations taking place in our Proxima-like corona and stellar from which we extract 3D snapshots of the entire simulation wind environment. As mentioned earlier, two similar TD flux-rope domain at a cadence of 1 minute. eruptions, only differing by nearly a factor of 2 in magnetic energy, serve to generate CME events in the regimes of weak (Figure 3) and partial (Figure 4) large-scale magnetic field confinement. 3. Results Following Alvarado-Gómez et al. (2019b),weemploya 3.1. Coronal Alfvén Speed Profiles density contrast n(t)/nSS=3.0 (with nSS as the pre-eruption local density value) to identify and the CME front.15 We use the We examine first the coronal Alfvén speed distributions positions of each point on this time-evolving isosurface to obtained in our steady-state solutions. Figure 1 compares the ( CME) calculate the maximum of the CME UR , and resulting VA on an arbitrary meridional projection, with a SW −1 to extract the steady-state pre-CME stellar wind (V ) and common color scale saturated between 15kms  VA  R − ( ) 10, 000 km s 1. Radial profiles for different regions/latitudes Alfvén VA speeds on the same locations in each time step. As are indicated and correspondingly plotted in Figure 2, together described before, this is necessary, as the CME motion needs to with the stellar wind speed (VSW) along the same profiles. be transformed to the stellar wind frame in order to check the nominal Alfvén shock condition: As expected, our simulated values of VA for the Sun—which are consistent with observations (see Zucca et al. 2014)— are globally lower than their stellar counterparts (by up to one ()UVCME - SW R R º>M CME 1.() 1 order of magnitude). The spatial distribution of VA also follows A VA the nominal behavior in the solar corona: large VA values very close to active regions (strong small-scale field) and above ( Additionally, by integrating over the volume enclosed by the coronal holes low-density sectors; see also Figure 2, top 16 panel). The lower V locations coincide with the high-density expanding front, taking into account the local escape velocity, A ( CME) ( CME) coronal streamers. Furthermore, the appearance of local we compute the mass M and EK of each CME 15 minima in VA above active regions, due to the superposition CME event. This procedure yields M1  9.4´ 10 g, of the small- and large-scale solar magnetic field, is also CME 32 EK,1  1.7´ 10 erg for the weakly suppressed CME captured in our simulation (see Mann et al. 2003). (Figure 3), and a partially suppressed eruption with M CME  The influence from a stronger large-scale magnetic field can 2 4.0´ 1015 g, E CME  3.2´ 1031 erg (Figure 4). be clearly seen in the stellar VA distributions (middle and K,2 bottom panels of Figure 1). A dipolar geometry is established, Figures 3 and 4 also include a visualization of the emerging fi shock regions through a distribution of spheres with size and with open- eld magnetic polar regions showing large VA CME values that gradually decrease toward the magnetic equator, color normalized by MA . Despite the difference in magnetic — fi where the density increases and the field strength decreases (see energy and therefore in the con nement imposed by the fi — also Figure 2, middle and bottom panels). Despite the large large-scale eld both events are able to generate shocks in the ( ) densities, the strong and ubiquitous small-scale field present in corona. As expected from the VA distribution Section 3.1 ,in both cases the super-Alfvénic region of the CME appears close our M-dwarf model increases VA close to the surface. As with to the current sheet. Relatively high M CME values appear the solar case, local minima in VA occur at different positions A and heights in the stellar corona. These are nearly absent in our 15 Sun-like simulation, where the large-scale magnetic field This threshold is usually not met during the first 1–2 minutes of evolution. fi In those cases, we consider instead 60% of the maximum value achieved in dominates the surface distribution. As the large-scale eld is n(t)/nSS. weaker in the Sun-like case, V decays more rapidly with 16 A Calculated as vGMHesc = 2 * , where G is the gravitational constant and distance compared to the M-dwarf solution. Still, this is only H is the front height from the stellar surface.

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Figure 2. Radial profiles of VA extracted from each of the AWSoM steady-state solutions (Figure 1, white lines). Active region (AR) and (CH) profiles are included for the solar case (top panel). Four latitudes are probed in our two stellar cases (middle and bottom panels). The stellar wind speed (VSW) along each profile is indicated by the color scale.

Figure 1. Meridional projection of the Alfvén speed (VA) in our AWSoM steady-state simulations. Top: Sun (CR 2107). Middle: young Sun-like star locally (a few tens), much larger than in solar observations (see, (CR 2107 + 75 G large-scale dipole). Bottom: M-dwarf (Proxima Centauri). e.g., Maguire et al. 2020). Still, most of the perturbation front fi ( ) The sphere represents the stellar surface, color-coded by the radial eld BR remains sub-Alfvénic as the eruption expands. These results driving each model. The color scaling for VA is preserved in all cases. The VA profiles in Figure 2 have been extracted along the white lines The field of view uniquely depend on the 3D setup of the simulations and would is 12 R★, with a set of selected magnetic field lines in black. not be found in a 1D case.

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fi ( FR 35 CME 32 CME 15 ) Figure 3. Snapshot during the temporal evolution of the weakly con ned CME EB,1  4.1´ 10 erg, EK,1  1.7´ 10 erg, M1  9.4´ 10 g within our M-dwarf simulation. The stellar surface is color-coded (purple-green) by the radial magnetic field driving the ambient AWSoM solution. A secondary color scale (magenta-yellow) denotes the density contrast, n(t)/nSS, which is used to trace the CME front by the indicated isosurface. The nominal shock condition, calculated ( CME  ( )) ( ) from the Alfvénic Mach number of the CME front MA , Equation 1 , is encoded simultaneously by the size of the scatter distribution spheres and by a tertiary color scale (cyan-red). The field of view is 32 R★, with a set of selected large-scale magnetic field lines in gray.

One significant difference between the simulated CME section, this will have important consequences for any TypeII events appears in the height with respect to the stellar surface of burst radio signatures induced by these shocks, and their the shock formation region (note that the field of view and detectability in the stellar regime with current instrumentation. timestamp in Figures 3 and 4 are different). All the other Finally, given the very large magnetic fields in the upper parameters of the TD flux-ropes being equal, this responds to corona, temperature effects due to heating at radius <10 R★ fi the available magnetic energy to power the eruption, which in can be neglected. We have veri ed that along the current sheet < turn determines the relative importance of the magnetic in the M-dwarf simulation the wind temperature is T 3 MK. suppression on the emerging eruption properties such as the The resulting speed, for an hydrogen ideal gas, is ∼   -1 ( ) 200 km s  VA, so that the fast magnetosonic Mach CME speed Alvarado-Gómez et al. 2018 . CME < To better illustrate this, Figure 5 shows averages over the number can be approximated with MA within 1%. A local CME front of the radial speed in the stellar wind frame larger temperature would push the distance of the transition to a CME SW super-Alfvénic CME speed further out by a modest amount. áUVR -ñR , and the local Alfvén speed áVAñ, as a function of distance in both events. The resulting global behavior shows that the sub- to super-Alfvénic transition, indicative of the 4. Discussion shock formation region, occurs at several stellar radii of height Solar type II radio bursts are typically divided by their for both events (roughly at 10 R★ and 20 R★ for the events in associated wavelength or starting frequency (see Sharma & Figures 3 and 4, respectively). As discussed in the following Mittal 2017 and references therein). Coronal type II radio

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fi ( FR 35 CME 31 CME 15 ) Figure 4. Snapshot during the temporal evolution of the partially con ned CME EB,2  2.0´ 10 erg, EK,2  3.2´ 10 erg, M2  4.0´ 10 g within our M-dwarf simulation. See the caption of Figure 3. Note the difference in field of view (45 R★) and timestamp (50 minutes) in this case. bursts manifest at decimeter to metric wavelengths (MHz 3 Re of height), and that the kinetic energy of the CME range), and interplanetary (IP) type II radio bursts appear at controls the lifetime of the radio emission (i.e., the range of decametric to kilometric wavelengths (kHz range). One frequencies covered by a given event). When the sample is fundamental aspect related to their detection is the fact that restricted to coronal type II radio bursts alone, Gopalswamy the impedes the transmission of radio waves with et al. (2005) reports that the average shock formation region is frequencies below ∼10MHz (cutoff frequency17). Therefore, even lower in height (<2 Re; see also Ramesh et al. 2012; only coronal typeII bursts are accessible from ground-based Gopalswamy et al. 2013). instrumentation, which is also the sole possibility for their Our analysis indicates that the shocks generated by the search in the context of stellar CMEs (see Villadsen 2017 and simulated M-dwarf CME events are pushed much farther out references therein). (see Figure 5). At such distances, the coronal densities have The type II radio burst division is clearly motivated by the decreased substantially compared to the standard formation expected shock formation region. Still, several solar events region of solar type II bursts, shifting their frequencies close to, display emission in the entire radio domain (meter-to-kilometer or below, the ionospheric cutoff. This is presented in Figure 6, type II bursts). Gopalswamy et al. (2005) studied the properties where the expected fundamental, np  8980 n [Hz], and first ν of meter-to-kilometer type II radio bursts and their driving harmonic, 2 p, of the plasma frequency are shown as a function CMEs. This statistical analysis revealed that the majority of of time. As regions with stronger shocks are expected to CME— such radio events form close to the solar surface (i.e., below contribute more to the global type II emission, MA weighted average densities are considered for this calculation. 17 This is a nominal average value which, among other factors, has diurnal, Nevertheless, Figure 6 shows that our simulated M-dwarf seasonal, and solar activity-related variations (see Yiǧit 2018). CMEs are not entirely radio-quiet. The expected fundamental

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Figure 5. Global Alfvénic regimes as a function of distance in our simulated M-dwarf CME events (left: weakly suppressed, Figure 3; right: partially suppressed, ) CME SW Figure 4 . In circles, and color-coded by simulation time, is the radial CME speed in the stellar wind frame áUVR - R ñ, spatially averaged over the expanding front. The mean Alfvén speed values áñVA , computed over the same spatial locations, are indicated by downward triangles. The nominal transition from sub-Alfvénic, CME CME ∼ áMA ñ<1, to super-Alfvénic, áMA ñ>1, is indicated. The spike in speed at a distance of 6.5 R★ in the right panel is due to the fragmentation of the CME, where the average speed is dominated by the outermost small fragments escaping the large-scale confinement (see Alvarado-Gómez et al. 2019a, 2019b).

representative for M-dwarfs, that corresponds to 1.4 mJy from Proxima Centauri’s distance of 1.3 pc, although this specific object in the Southern sky is not visible to LOFAR with a core location at a geographic latitude of 53° north. LOFAR provides online tools for sensitivity estimates.18 For an observing frequency around 30 MHz, a maximum burst duration of 30 minutes, and a typical instantaneous burst bandwidth of 20 MHz (Morosan et al. 2019), this leads to a sensitivity of just 5 mJy. And this number has to be treated with caution, since this estimate does not consider effects like calibration errors, ionospheric conditions, elevation of the source, and errors in beam models. The application of a factor of 5 is advised. So it has to be concluded that even in the best case, i.e., harmonic emission from the weakly confined case in the upper panel of Figure 6, with a total flux equal to the maximum solar value, CME-related type II radio burst emission cannot be observed by LOFAR even for the nearest M-dwarfs. The upcoming (SKA), with its eponymous collecting area, could provide the necessary sensitivity and also geographic location for observations of Proxima Centauri. However, the lowest frequency band of SKA just starts at 50 MHz (Nindos et al. 2019). From Figure 6 it follows that there is no radio emission from frequencies above 50 MHz, as the sources of both fundamental and harmonic emission would Figure 6. Temporal evolution of the expected type II radio burst frequencies be located in the region where the CME is still sub-Alfvénic. associated with the shock regions in our simulated M-dwarf CMEs (Top: In agreement with the results of Mullan & Paudel (2019),we fi — fi — ) weakly con ned Figure 3; bottom: partially con ned Figure 4 . The find then that the ground-based detection of stellar CMEs via fundamental (np  8980 n [Hz]) and first harmonic (2νp) of the plasma CME type II burst emission would be greatly hampered by the frequency are included. The associated MA - weighted mean plasma density is indicated by the color scale. Gray regions denote the intervals in which each combined effect from magnetic suppression and large VA CME is within the sub-Alfvénic regime (see Figure 5). values in the corona. It is worth noting that our Proxima Centauri background steady-state model already provides a fi and harmonic type II burst frequency drifts, generated by the best-case scenario: a lower bound on the mean surface eld strongest eruption considered here (Figure 6, top panel), remain strength (∼450G; Reiners & Basri 2008), the highest stellar (   above the ionospheric cutoff for ∼10 minutes and ∼30 wind density allowed by observations M  0.3 M; Wood minutes, respectively. With approximately ∼80% less kinetic et al. 2001), and a CME shock trajectory following the current ( SW energy, only a ∼15 minutes harmonic lane clears this threshold sheet i.e., global minimum of VA and low V ; see the bottom in the weaker CME event (Figure 6, bottom panel). panels of Figures 1and 2). Still, our analysis shows that the We now estimate whether such stellar type II radio bursts required CME speed of 10% the speed of light, suggested by could be detected with ground-based instruments like the LOw Mullan & Paudel (2019) for Proxima-like surface magnetic Frequency ARray (LOFAR, van Haarlem et al. 2013). The fields, is overestimated. This most likely reflects the lower strongest solar type II radio bursts reach spectral fluxes up to 108 Jy (Schmidt & Cairns 2016). If we assume that this is also 18 https://support.astron.nl/ImageNoiseCalculator/sens.php

8 The Astrophysical Journal, 895:47 (10pp), 2020 May 20 Alvarado-Gómez et al. dimensionality and much simpler coronal model assumed in and made available through the NASA Community Coordi- their study. nated Modeling Center (CCMC). Resources supporting this In terms of our simulated eruptions, the kinetic energies work were provided by the NASA High-End Computing appear conservative with respect to the range determined for (HEC) Program through the NASA Advanced Supercomputing the best CME candidate observed in Proxima Centauri so far (NAS) Division at . Simulations were ( × 29 CME 34 ) ’ 1 10 erg < EK <´410erg; Moschou et al. 2019 . performed on NASA s Pleiades cluster under award SMD- Leaving aside considerations on occurrence rate, more 17-1330. energetic CMEs might be able to shock higher density regions Facility: Pleiades. closer to the stellar surface, increasing the radio frequency of Software: SWMF (Gombosi et al. 2018). the associated type II bursts. However, kinetic energies of CMEs appear correlated with small-scale surface magnetic flux in solar observations (e.g., Toriumi et al. 2017; Sindhuja & ORCID iDs Gopalswamy 2020). If such a relation holds for stellar CMEs, it Julián D. Alvarado-Gómez https://orcid.org/0000-0001- implies that VA could also increase locally for stronger 5052-3473 eruptions, again creating unfavorable conditions for the Jeremy J. Drake https://orcid.org/0000-0002-0210-2276 generation of shocks in the low corona. Still, this effect might Federico Fraschetti https://orcid.org/0000-0002-5456-4771 be secondary for certain large-scale magnetic field strengths Cecilia Garraffo https://orcid.org/0000-0002-8791-6286 (i.e., reduced CME suppression). Future investigation will be Ofer Cohen https://orcid.org/0000-0003-3721-0215 pursued in this direction, expanding the parameter space to Christian Vocks https://orcid.org/0000-0001-8583-8619 additional spectral types, surface magnetic field configurations, Katja Poppenhäger https://orcid.org/0000-0003-1231-2194 stellar wind properties, and CME eruption models. Sofia P. Moschou https://orcid.org/0000-0002-2470-2109 Rakesh K. Yadav https://orcid.org/0000-0002-9569-2438 // / 5. Summary Ward B. Manchester IV https: orcid.org 0000-0003- 0472-9408 Continuing our numerical investigation on stellar CMEs, we have considered here the expected connection between these eruptive phenomena and the generation of type II radio bursts. References Using physics-based 3D MHD corona and stellar wind models, we compared the Alfvén speed distribution for the Alvarado-Gómez, J. D., Drake, J. J., Cohen, O., Moschou, S. P., & Garraffo, C. 2018, ApJ, 862, 93 Sun, a young Sun-like star, and a moderately active M-dwarf. Alvarado-Gómez, J. D., Drake, J. J., Garraffo, C., et al. 2019a, arXiv:1912. We examined the regions where the Alfvén and stellar wind 12314 speeds provide the most favorable conditions for the generation Alvarado-Gómez, J. D., Drake, J. J., Moschou, S. P., et al. 2019b, ApJL, of shocks in the corona. Furthermore, employing a state-of-the- 884, L13 fl Alvarado-Gómez, J. D., Garraffo, C., Drake, J. J., et al. 2019c, ApJL, 875, L12 art ux-rope eruption model, we simulated admissible CME Argiroffi, C., Reale, F., Drake, J. J., et al. 2019, NatAs, 3, 742 events occurring in the archetypal star Proxima Centauri. We Benz, A. O. 2017, LRSP, 14, 2 considered two eruptions representative of the regimes over Bilenko, I. A. 2018, Ge&Ae, 58, 989 which the ejected plasma is able to escape the large-scale Cairns, I. H., Knock, S. A., Robinson, P. 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